Question

Problem 1. For the problems below determine the error in the solution at t=10 and t=20...

Problem 1. For the problems below determine the error in the solution at t=10 and t=20 because of an error of ε in the initial condition..

  1. x’ = x, correct initial condition x(0)=c; initial condition with error x(0)=c+ε.
  2. x’ = -x, correct initial condition x(0)=c; initial condition with error x(0)=c+ε.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For problems 3-6, note that if y(t) is a solution of the homogeneous problem, then y(t−t0)...
For problems 3-6, note that if y(t) is a solution of the homogeneous problem, then y(t−t0) is a solution as well, where t0 is a fixed constant. So, for example, the general solution of a problem with complex roots can be expressed as y(x) = c1e µ(t−t0) cos(ω(t − t0)) + c1e µ(t−t0) sin(ω(t − t0)) When initial conditions are given at time t = t0 and not t = 0, expressing the general solution in terms of t −...
In the following problems determine whether existence of at least one solution of the given initial...
In the following problems determine whether existence of at least one solution of the given initial value problem is thereby guaranteed and if so, whether the uniqueness of that solution is guaranteed. For each initial value problem determine all solutions and the intervals where they hold, if the case. (a) dy/dx = y^(1/3); y(1) = 1. (b) dy/dx = y^(1/3); y(1) = 0. (c) dy/dx =sqrt(x - y); y(2) = 1. Can you explain how can we approach these kind...
Choose C so that y(t) = −1/(t + C) is a solution to the initial value...
Choose C so that y(t) = −1/(t + C) is a solution to the initial value problem y' = y2 y(2) = 3. Verify that the given formula is a solution to the initial value problem. x′ = −y, y′ = x, x(0) = 1, y(0) = 0: x(t) = cost, y(t) = sin t
1. a) Show that u(x, t) = (x + t) 3 is a solution of the...
1. a) Show that u(x, t) = (x + t) 3 is a solution of the wave equation utt = uxx. b) What initial condition does u satisfy? c) Plot the solution surface. d) Using (c), discuss the difference between the conditions u(x, 0) and u(0, t).
Consider the initial value problem given below. y' = (x+y+1)2 , y(0)= -1 The solution to...
Consider the initial value problem given below. y' = (x+y+1)2 , y(0)= -1 The solution to this initial value problem crosses the x-axis at a point in the interval [0, 1.4]. By experimenting with the improved Euler's method subroutine, determine this point to two decimal points.
1) x(t+2) = x(t+1) + x(t) , t >=0 determine a closed solution (i.e. a solution...
1) x(t+2) = x(t+1) + x(t) , t >=0 determine a closed solution (i.e. a solution dependent only on time t ) for above eqn. Verify your answer by evaluating your solution at t = 0 , 1, 2, 3, 4, 5. We are given x(0) = 1 and x(1) = 1
Solve the initial value problems in Exercises 11–20 for r as a vector function of t....
Solve the initial value problems in Exercises 11–20 for r as a vector function of t. 15. Differential equation: dr/dt = (tan t)i +(cos(t /2 ))j - (sec(2t))k Initial condition: r(0) = 3i - 2j + k
Problem 5 Solve the following initial value problems: 1. x′+(5/t)x=1+t, x(1)=1 2. x′ =(a+b/t)x, x(1)=1
Problem 5 Solve the following initial value problems: 1. x′+(5/t)x=1+t, x(1)=1 2. x′ =(a+b/t)x, x(1)=1
dx/dt=(1/4)x^3 -x, c(0)=1 compute the solution to this initial value problem. An algebraically implicit solution for...
dx/dt=(1/4)x^3 -x, c(0)=1 compute the solution to this initial value problem. An algebraically implicit solution for x(t) is acceptanle x(0)=1
Find the solution of each of the following initial-value problems. x'=y+f1(t), x(0)=0 y'=-x+f2(t), y(0)=0
Find the solution of each of the following initial-value problems. x'=y+f1(t), x(0)=0 y'=-x+f2(t), y(0)=0
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT